Question

how does (tan^-1(x))/x = 1 as x approaches 0?

Answer 1

tan-1 is a ratio of the value of an angle; as the ratio of the angle gets smaller; we get a one on one effect that settles into something more aking to 1

Answer 2

when an angle = 0 , then tangent = 0;

Answer 3

well, i should tried to drawn up an inverse tan; but same effect

Answer 4

the closer to 0 we get; the closer to x/x we get

Answer 5

remember, as limits go, we dont give a hoot about the value at "0" in this case; only what the value is approaching

Answer 6

yes, but i need to know algebraically how to turn tan^-1 to a different ID so that when i plug in 0 for x it equals 1

Answer 7

you might need more room than a single post can provide then :)

Answer 8

tan-1 is an angle; a radian between -pi/2 and pi/2

Answer 9

i cant think of any effective means of turning a ratio of y/x into a suitable alternative for algebraing

Answer 10

like a different trig identity?

Answer 11

\[tan^{-1}(x)=y\]
\[x=tan(y)\]
\[tan(y)/x\ ???\]

Answer 12

that might be good, since x = tan(y) :)
\[tan(y)\tan(y)\ ???\]

Answer 13

i had a division in there:
\[\lim_{x->0}\frac{tan(y)}{tan(y)}=1\]
thats the best I can think of ... which may not hold water

Answer 14

its bad form; tan-1(x) = y so we cant really replace it; bummer
\[\frac{y}{tan(y)}\]is a better rendition

Answer 15

cant see a comparison here either